Prevent Steering Actuator from over-shooting? BGE
You can increase the number of frames per second your game calculates. The steering actuator works by calculating the needed rotation to reach the target for each logic tic. The faster an object is moving, the more moment per tic it has along its axis. Each tic, it moves the object along an axis and calculates the rotation needed to reach the target. When the moment is fast, it adds a lot of distance and calculates the new rotation. If that distance is long enough to move your object off it's target path, it will look like it is overshooting.



By increasing the frames per second that the game runs at, you will increase the logic tics per second. This helps because it calculates a new rotation faster, keeping it on the target path better. 



For example, you could set it to 120 instead of 60. Your object should now recalculate it's rotation and trajectory along the path twice as fast. However - this will also drag down performance. The faster you set the FPS, the more work your computer needs to do. If you have a lot of logic, forcing it to run twice as fast should create a noticeable drain on performance.